The p-adic local Langlands correspondence for GL 2 (Qp) is given by an exact functor from unitary Banach representations of GL 2 (Qp) to representations of the absolute Galois group G Qp of Qp. We prove, using characteristic 0 methods, that this correspondence induces a bijection between absolutely irreducible non-ordinary representations of GL 2 (Qp) and absolutely irreducible 2-dimensional representations of G Qp . This had already been proved, by characteristic p methods, but only for p ≥ 5.1 18 Contrary to [17], all results of [21] are proved for all primes p.